Topics
3. Multiplication and division
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Australia
Year 5

3.09 Story problems

Lesson
Practice
Lesson

Are you ready?

We've seen how to write a  multiplication or division problem  , by finding clues in our story problems, such as sharing, or groups of.

Examples

Example 1

Dylan has 120 chocolates to give out to 10 guests at his birthday party and wants to make sure each guest gets the same amount.

Write a number sentence for this story problem to find how much each guest would get.

Worked Solution
Create a strategy

Dylan needs to equally share the chocolates, so we need to use division.

Apply the idea

Dylan needs to share or divide 120 chocolates into 10 equal groups. So he needs to divide 120 by 10.

Number sentence =120\div 10

Idea summary

If we know our total and want to find out how many groups we have, or how many are in each group, we need to divide.

Story problems with multiplication and division

We may see some different clues in our story problems, so we need to figure out if we need to multiply or divide.

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Examples

Example 2

An apartment block is 36 metres tall and a house is 6 metres tall.

How many times smaller is the house than the apartment block?

Worked Solution
Create a strategy

We need to use division to write the number sentence.

Apply the idea

To see how many times 6 fits into 36 we need to divide.

\displaystyle \text{Number of times smaller}\displaystyle =\displaystyle 36\div 6Divide 36 by 6
\displaystyle =\displaystyle 6
Idea summary

For story problems, we need to look for key words that tell us what we need to do.

Written problems with division

Let's look at some written problems, and rewrite them as number problems. We also solve a problem where we need to change some of our information into a value we can use.

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Examples

Example 3

Max's Motors sold 49 cars in a 7-day week.

a

If they sold the same number of cars every day, write a number sentence to show how many cars they sold each day. Use the (\div) symbol.

Worked Solution
Create a strategy

Divide the number of cars by the number of days.

Apply the idea

They need to divide 49 cars into 7 days.

\text{Cars each day }= 49 \div 7

b

How many cars were sold each day?

Worked Solution
Create a strategy

Perform the division from part (a).

Apply the idea

49 \div 7 = 7, so there were 7 cars sold each day.

Idea summary

If we have a total to share, we use division to work out how many groups, or how many in each group.

Written problems with remainders

When you are solving division story problems, you may still end up with a remainder.

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Examples

Example 4

A show bag costs \$7.

a

How many show bags can I buy with \$31?

Worked Solution
Create a strategy

Divide the total amount of money by the cost of each bag.

Apply the idea

31\div 7 = 4 remainder 3.

We cannot buy part of a show bag. So we can only buy 4 show bags.

b

How much money will I have left over?

Worked Solution
Create a strategy

Subtract the cost of 4 show bags from the total money.

Apply the idea

First we need to find the cost of 4 show bags.

\displaystyle \text{Cost}\displaystyle =\displaystyle 4 \times \$7Multiply the number of bags by the price
\displaystyle =\displaystyle \$28

Now we can subtract this from the \$31 they had at the beginning.

\displaystyle \text{Left over money}\displaystyle =\displaystyle 31 - 28Subtract \$28 from \$31
\displaystyle =\displaystyle \$3
Idea summary

  • Words that suggest finding the total of a number of equally sized groups of something indicate multiplication.

  • Words that suggest sharing into equal groups will require us to use division.

Outcomes

ACMNA100

Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies

ACMNA101

Solve problems involving division by a one digit number, including those that result in a remainder

ACMNA291

Use efficient mental and written strategies and apply appropriate digital technologies to solve problems

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